Image sensor calibration

ABSTRACT

A method of calibrating an image sensor may include detecting a response from a pixel of the image sensor as a result of light having an intensity impinging on the pixel, and measuring the actual standard deviation of the response of the pixel at the intensity of light. The method may also include determining an averaging number for the pixel at the intensity. The averaging number may be a number of responses of the pixel at the intensity to be averaged to attain an average response having a standard deviation less than or equal to a target value. The method may further include determining the average response of the pixel using the determined averaging number.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of priority from U.S. ProvisionalApplication No. 61/771,550, filed on Mar. 1, 2013, the entirety of whichis incorporated by reference herein.

TECHNICAL FIELD

Embodiments of the invention relate generally to systems and methods ofcalibrating an image sensor of a device, and image sensors and devicesthat employ the calibration technique.

BACKGROUND

An image sensor is a device that converts an optical image into anelectronic signal. Image sensors are used in imaging devices, such as,for example, digital cameras to capture an optical image. Commonly usedimage sensors include digital charge-coupled device (CCD) orcomplementary metal oxide semiconductor (CMOS) active pixel sensors.These image sensors generate a flow of electrons (which manifests ascurrent, voltage, etc.) that is indicative of the intensity of lightthat impinges on the sensor. Based on the response (current, voltage, orother indicator) of the image sensor, the amount of light incident onthe sensor can be measured. An image sensor includes an array ofindividual pixels that are arranged thereon. Each of these pixelsrespond differently to incident light, due to manufacturing variations(e.g., semiconductor processing variation) and random or “shot” noise.The response of each pixel also fluctuates as a function of theintensity of the light that falls on the pixel due to noise. Themanufacturing related variations in light response of pixels manifestsas spatial variations in the response of an image sensor, and theintensity related variations manifests as temporal variations in theresponse of an image sensor. The spatial and temporal variation in theresponse of an image sensor is undesirable in imaging applications.Although calibration techniques can be applied to correct the spatialvariations in light response of an image sensor, known calibrationtechniques do not adequately account for the temporal variations in theimage sensor. Consequently, for some applications, calibrationtechniques used to correct the light response of an image sensor can beunacceptably inaccurate. The systems and methods of the presentdisclosure may help address the foregoing problems and/or other problemsexisting in the art.

SUMMARY

In one embodiment, a method of calibrating an image sensor is disclosed.The method may include detecting a response from a pixel of the imagesensor as a result of light having an intensity impinging on the pixel,and measuring the actual standard deviation of the response of the pixelat the intensity of light. The method may also include determining anaveraging number for the pixel at the intensity. The averaging numbermay be a number of responses of the pixel at the intensity to beaveraged to attain an average response having a standard deviation lessthan or equal to a target value. The method may further includedetermining the average response of the pixel using the determinedaveraging number.

Various embodiments of the invention may include one or more of thefollowing aspects: receiving the actual standard deviation may includedetermining the actual standard deviation of the response of the pixelat multiple intensities of incident light and recording the determinedactual standard deviations; determining the actual standard deviationmay include determining the actual standard deviation for multiplepixels of the image sensor at multiple intensities of incident light andrecording the determined actual standard deviations; determining theaveraging number may include determining an averaging number for each ofthe multiple pixels, the averaging number for each pixel of the multiplepixels maybe the number of the responses of the pixel to be averaged toattain an average response for the pixel at the intensity of lightincident on the pixel; determining the averaging number may includedetermining the averaging number using the equationn=ceil[(σ_(actual)/(σ_(target))²], where n=the averaging number,σ_(actual)=the actual standard deviation of all pixels at the intensity,σ_(target)=the target value of standard deviation, and ceil is a ceilingfunction that rounds a result of (σ_(actual)/(σ_(target))² to the nextinteger greater than or equal to the result.

Various embodiments of the invention may also include one or more of thefollowing aspects: determining the averaging number may include roundingthe determined averaging number to the closest higher power of two; therounding may include rounding the determined averaging number using theequation n*=2 to the power of (ceil[log₂(n)]), where n*=the averagingnumber rounded to the closest higher power of two, n=the determinedaveraging number, and ceil is a ceiling function that rounds a result ofthe calculation to the next integer greater than or equal to the result;the target value of standard deviation may be the actual standarddeviation of a pixel of the image sensor having a lowest value ofresponse; and the target value of standard deviation maybe 1 DN.

In another embodiment, a control system for an image sensor isdisclosed. The control system may include an image sensor including aplurality of pixels arranged thereon. Each pixel of the plurality ofpixels being configured to output a response indicative of an intensityof light incident thereon. The control system may also include a memoryincluding a database. The database may include an averaging number forat least one pixel of the plurality of pixels at multiple intensities.The averaging number may be indicative of a number of responses of thepixel at an be averaged to attain an average response having a standarddeviation less than or equal to a target value. The control system mayalso include a processor operatively coupled to the image sensor and thememory. The processor may be configured to determine the averageresponse of the pixel based on the determined averaging number and theintensity of light incident on the pixel.

Various embodiments of the control system may include one or more of thefollowing aspects: wherein the database may include the averaging numberfor each of multiple pixels of the plurality of pixels; the processormay be configured to determine the averaging number for the multiplepixels, the averaging number for each pixel of the multiple pixels maybe the number of the responses of the pixel to be averaged to attain anaverage response for the pixel at the intensity of light incident on thepixel; the database may include the averaging number obtained using theequation n=ceil[(σ_(actual)/(σ_(target))], where n=the averaging number,σ_(actual)=the actual standard deviation of all pixels at the intensity,σ_(target)=the target value of standard deviation, and ceil is a ceilingfunction that rounds a result of (σ_(actual)/(σ_(target))² to the nextinteger greater than or equal to the result; the database may includethe averaging number rounded to the closest higher power of two; and thecontrol system may further include an endoscope coupled to the imagesensor.

In a further embodiment, a method operating an image sensor isdisclosed. The method may include detecting a response from a pixel ofthe image sensor as a result of light having a first intensity impingingon the pixel. The method may also include obtaining an actual standarddeviation of the response of the pixel at the first intensity. Theactual standard deviation may be a number indicative of an expectedvariation in the response of the pixel. The method may also includedetermining a number n at the first intensity, wherein the number n isthe number of frames at the first intensity to be averaged to attain atarget standard deviation for the response at the first intensity. Themethod may further include averaging n number of responses from thepixel at the first intensity to obtain an average response from thepixel at the first intensity.

Various embodiments of the method may include one or more of thefollowing aspects: obtaining the actual standard deviation may includereceiving the actual standard deviation from a memory operativelycoupled to the image sensor; determining the number n may use aprocessor operatively coupled to the image sensor; and detecting theresponse may include detecting the response from the image sensor of anendoscope.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic diagram of an endoscope including an imagedetector, according to an embodiment of the invention.

FIG. 2 is a schematic of an exemplary image sensor of the endoscope ofFIG. 1.

FIG. 3 is a schematic graph that illustrates the responsivity of anexemplary pixel of the image sensor of FIG.

FIG. 4 is an exemplary illustration, of the variation of the number offrames of a pixel to be averaged, as a function of incident lightintensity, for a response with a desired noise level.

DETAILED DESCRIPTION

The systems and methods disclosed herein can be applied to an imagesensor used in any application. However, as one exemplary applicationthe discussion that follows, an image sensor applied in an endoscopicapplication is described.

FIG. 1 is a schematic diagram that illustrates an exemplary endoscope100 including an exemplary image sensor 104 coupled to the distal end108 of an elongate body 102. The image sensor 104 may be any type ofimage sensor, such as for example, CCD, CMOS, etc., known in the art.Image sensor 104 may generate a signal indicative of the intensity oflight 105 (or another type of electromagnetic radiation) that impingesthereon. Image sensor 104 may include one or more image detectingelements (“pixels”) arranged in any pattern thereon. In use, the distalend 108 of the endoscope 100 may be inserted into a human body andpositioned proximate a work site (such as, for example, an ulcer) withinthe body. Thus positioned, image sensor 104 may be adapted to acquire animage of the work site. This image may be transmitted and displayed onan image device 120 positioned outside the body. Endoscope 100 may alsoinclude a control system 150 configured to control the operation of theimage sensor 104. In some embodiments, control system 150 may beintegrated with a control system that controls other operations of theendoscope 100. Control system 150 may include, among other components, aprocessor 112 configured to perform image processing applications and amemory 114 configured to store a database of values. Although controlsystem 150, memory 114, and processor 112 are illustrated as beingseparate from endoscope 100, in some embodiments, some or all of thesecomponents may be integrated. Further, although the display device 120and control system 150 are illustrated as being coupled to image sensor104 using a wire, this is only exemplary. In some embodiments, displaydevice 120 and/or control system 150 may be wirelessly coupled to theimage sensor 104. Image sensor 104 may include an array of pixelsarranged in a pattern.

FIG. 2 is a schematic illustration an exemplary array of pixels 122 inimage sensor 104 of endoscope 100. Although a 2-dimensional array ofpixels 122 arranged in a planar configuration is illustrated in FIG. 2,this is only exemplary. In some embodiments, the pixels 122 of an imagesensor 104 may be arranged in another configuration (for example, aone-dimensional array arranged on a curved surface). Each pixel 122 ofthe image sensor 104 may generate a signal that is indicative of theintensity of the light impinging on that particular pixel. The signalmay be an analog or a digital signal. In some embodiments, the imagesensor 104 may include electronics (such as an A/D converter) thatoutputs a digital number (DN) that is indicative of the intensity of thelight incident on pixel 122. The magnitude of the digital number maydepend upon the type of image sensor 104 and/or the includedelectronics. For example, image sensors 104 and/or related electronicsbased on 8 bit integrated circuit devices may output digital numbersvarying from 2° (1) to 2⁸ (256) in response to light that is incidentthereon. In such embodiments, the magnitude of the DN that is output bypixel 122 may vary proportionately as a function of the intensity oflight incident on the pixel 122.

In some embodiments, the image sensor 104 may be referred to as a pixelarray, a multidimensional pixel array, a pixel matrix, or an imager.Although not shown, the image sensor 104 may include devices (forexample, for separating and/or detecting different spectral regions oflight) such as a Bayer sensor, a dichroic prism, etc, that may becommonly used with image sensors. The spectral region of light, in someembodiments, may be a continuous or a discontinuous (e.g., periodic,irregular) band of wavelengths centered around a specific wavelength.For example, the band of wavelengths can be centered around a visiblecolor wavelength such as a red wavelength or a green wavelength.

The pixels of image sensor 104 may be configured to be individuallycalibrated to account for variations in the response of each pixel toincident light 105. A pixel can be calibrated by calculating one or morecalibration factors that may be used to modify the response of the pixelto match a target response. The calibration factor can be used to adjusta response of a pixel such that the response corresponds with a targetresponse at a specified intensity of light 105 incident on the pixel.The response of a pixel (or an image sensor) to a range of lightintensities is referred to as responsivity. The responsivity of a pixelmay be expressed as a curve that plots the variation of the pixelresponse as a function of light intensity. In general, the responsivitymay be linear or non-linear, hi some embodiments, different calibrationfactors can be calculated for pixels that have different responsecharacteristics (e.g., different inherent response characteristics) overa range of intensity values of incident light 105. In other words, oneor more calibration factors can be calculated for one or more pixelsfrom an image sensor to account for spatial variations across the imagesensor.

In some embodiments, a calibration factor associated with a pixel can becalculated using a calibration algorithm such as a single-pointcalibration algorithm or a multi-point calibration algorithm (i.e.,calibration based on two or more calibration points). For convenience,the embodiments described in this detailed description focus on atwo-point calibration algorithm, but the methods and apparatus describedherein can be applied to different calibration algorithms such as athree-point calibration algorithm. In a two-point calibration algorithm,two sets of pixel-response values of a pixel that are respectivelyassociated with two different intensity values are used to define alinear response-intensity relationship. The number (e.g., one or more)of pixel-response values in each set is referred to herein as the datapoint number. In some embodiments, the data point number may be referredto as a calibration number or a frame number, and has integer valuessuch as, for example, 1, 2, 3, 4, 8, 12, 16, etc. The response-intensityrelationship can be representative of the response of the pixel over arange of intensity values associated with the two different intensityvalues. A correction or a calibration factor can be calculated based ona difference(s) between the response-intensity relationship and a targetresponse-intensity relationship such that a pixel-response valuemodified based on the calibration factor will substantially correspondto the target response-intensity relationship. In some embodiments, eachset of pixel-response value can have different numbers of pixel-responsevalues as defined by the data point numbers.

To increase the probability that a response-intensity relationship willbe a substantially accurate model of the responsivity of a pixel, thenumber of data points in the sets of pixel-response values can becalculated based on a statistical threshold condition(s) (e.g., astandard-deviation condition(s), a standard-deviation limit/value(s), ora confidence interval condition(s)). The statistical threshold limit canbe defined such that one or more data point numbers can be calculatedand used in a two-point calibration algorithm to modify (e.g., increaseor decrease) the confidence that a calibration factor calculated usingthe two-point calibration algorithm can substantially account fordifferences between a response-intensity relationship associated withpixel and a target response-intensity relationship.

In some embodiments, the data point number can be calculated such that aresponse-intensity relationship defined based on the data point numberwill have a specified probability of representing an inherentresponse-intensity relationship of a pixel (e.g., response-intensityrelationship without temporal noise). In some embodiments, one or moredata point numbers can be calculated to increase or decrease theprobability that a response-intensity relationship defined based on thedata point number in a two-point calibration algorithm will berepresentative of an inherent response-intensity relationship of apixel. In some embodiments, the data point number(s) may be selected todecrease the influence of scatter (e.g., statistical outliers) in thecalibration algorithm. The scatter or distribution of pixel-responsevalues can be caused by, for example, temporal noise or noise associatedwith instruments used to acquire the pixel-response values at thecalibration points of the two-point calibration.

In some embodiments, the processor 112 of endoscope 100 may beconfigured to calculate a response-intensity relationship(s) and/or acalibration factor(s) associated with the image sensor 104. Theprocessor 112 may be operatively coupled and configured to access thememory 114. The memory 114 may be configured to store the calibrationfactor(s) and/or a target response-intensity relationship used tocalculate the calibration factor(s). The memory 114 can also beconfigured to store instructions that can be accessed by and/or executedby the processor 112. In some embodiments, the instructions can beconfigured to trigger the processor 112 to use one or more calibrationfactors to modify a responsivity of the image sensor 104.

FIG. 3 is an exemplary graph 300 illustrating the responsivity of pixel122 of image sensor 104. The x-axis of graph 300 indicates the intensityof light 105 impinging on the pixel 122, and they-axis of graph 300indicates the response of the pixel 122 (in digital number, DN) at thedifferent light intensities. The x-axis of graph 300 also identifies twolight intensities (marked “intensity A” and “intensity B”), at whichframes of images may be acquired to calculate calibration factors tominimize the temporal variation of the response of pixel 122. The lightintensities at intensity A and intensity B may be any value. In thediscussion that follows, the intensity of light at the intensity A isassumed to be lower than the intensity of light at intensity B. Severalframes of images (that is, data point numbers) may be acquired usingimage sensor 104 at intensities A and B. Points 382 a, 382 b, 382 crepresent the response of pixel. 122 (in DN) corresponding to frames atintensity A, and points 384 a, 384 b, 384 c, and 384 d represent theresponse of pixel 122 corresponding to frames at intensity B. Asillustrated in graph 300, the standard deviation or the scatter of theresponse, σ_(A), at intensity A is lower than the standard deviationσ_(B) of the response at intensity B. This trend in the standarddeviation is observed because noise is known to be proportional to theintensity of the illumination That is, the noise associated with abrighter image is known to be larger than noise associated, with adarker image. In some embodiments, linear regression (or anothersuitable procedure) may be used to approximate the response of the pixel122 at intensities between intensity A and intensity B. Lines 322 and324 of graph 300 illustrate the upper and lower bounds of the responseat different intensities between intensity A and intensity B. That is, aresponsivity relationship derived based on two random intensities(intensity A and intensity B) may fall anywhere within the upper bound322 and lower bound 324.

It is known that noise at an illumination level can be reduced byaveraging several frames taken at the illumination level. The larger thenumber of frames that are averaged, the lower is the noise. That is, byaveraging the response of the pixel 122 from several frames taken at anillumination level, the error associated with noise (or temporalvariation) at that illumination level may be minimized. Therefore, byaveraging several frames taken at intensity A, an average value of theresponse with minimal noise may be obtained. Similarly, averagingseveral frames taken at intensity B, an average value of the response atintensity B with minimal noise may be obtained. However, since theinherent standard deviation of the response at high intensities isgreater than that at low intensities (that is, σB>σ_(A)), a largernumber of frames will have to be averaged at the intensity B than atintensity A for comparable noise reduction. In embodiments whereaveraging a certain number of frames (for example, three frames) atintensity A reduces σ_(A) by an acceptable amount, averaging the numberof frames at the second calibration intensity may not reduce σ_(B)sufficiently for acceptable noise reduction. Averaging a large number offrames at all intensity levels may minimize the noise. However,increasing the number of frames to be averaged is computationallyexpensive. Therefore, it is desirable to average only the number offrames that is required to minimize noise to an acceptable level.

The acceptable level of noise (Os acceptable, desired, or targetstandard deviation) may depend upon the application. In someembodiments, an acceptable value of noise may be the lowest amount ofnoise in an image. For example, with reference to FIG. 3, in someembodiments, the acceptable level of noise may be the noise, or thestandard deviation, of the response at intensity A (that is, ox). Insuch an embodiment, it may be desirable to average as many number offrames at intensity B to reduce the standard deviation of the responseat intensity B to about σ_(A). Decreasing the standard deviation of theresponse at intensity B to be approximately the same as the standarddeviation, of the response at intensity A will make the noise level atboth locations to be about the same. In some embodiments, the acceptablelevel of noise may be based on standard deviation of the response of thepixel with the lowest level of illumination (that is, lowest DN output).Since the noise associated with a dark image is low, selecting the noiselevel associated with the darkest pixel as the acceptable standarddeviation of noise makes the noise all illumination s in an image to bethe least. In some embodiments, the acceptable value of noise may beselected to be the smallest change that can be detected by a pixel.Since 2°, or 1 DN, is the smallest digital number that can output by apixel or its associated electronics, a change in response of less than 1DN cannot be recognized by the control system 150. Therefore, in someembodiments, the acceptable level of noise may be considered to be 1 DN.

In some embodiments of the current disclosure, the control system 150may determine the number of frames to be averaged at an intensity levelto reduce the standard deviation of the response to target value (thatis, reduce the noise to the acceptable level). In some embodiments, thecontrol system 150 may use an algorithm that computes the number offrames “n” to be averaged at any particular light intensity usingequation 1 below:

$\begin{matrix}{n = {{ceil}( \frac{\sigma_{actual}}{\sigma_{target}} )}^{2}} & (1)\end{matrix}$

where σ_(target) is the desired or the target standard deviation value,and σ_(actual) is the actual standard deviation of the response at thatparticular light intensity. Ceil is a ceiling function that rounds theresult of the calculation, for example, A, to the nearest integergreater than or equal to A. That is, if the standard deviation or thescatter of pixel 122 at any given light intensity is known, equation 1provides the number of frames that will ha be averaged to attain aresponse having a target standard deviation (or scatter level). Thenumber or frames “n” may vary with the intensity of illumination. Ingeneral, since the standard deviation of the response increases withlight intensity, more frames may need to be averaged at higher lightintensities to obtain the same target standard deviation as a responseat a lower light intensity.

The standard deviation of pixel 122 at any intensity (σ_(actual)) may bedetermined based on experimentation or may be otherwise known apriori.In some embodiments, the standard deviations of each pixel at differentlight intensities may be stored in a database in memory 114 of controlsystem 150. In some embodiments, memory 114 may maintain a database of“n” values for each pixel of light sensor 104 at different intensities.And, based on the observed response of each pixel in an application, thecontrol system 104 may determine, Me, or obtain from the database, thenumber of frames “n” that will need to be averaged to reduce the noiseto the acceptable standard deviation (σ_(target)). Based on thisinformation, the processor 112 of the control system 120 may beconfigured to average the required number of frames to reduce the noiseto the acceptable level. In some embodiments, the database may store the“n” values of each pixel at several desired standard deviation values(σ_(target)). In such embodiments, a user may select the σ_(target)value to use in an application, and the control system may choose avalue of “n” that corresponds to the observed intensity and the userselected σ_(target) value.

In embodiments where image sensor 104 includes several million pixels,the computational burden of averaging several frames of each pixel maybe high. Therefore, in some embodiments, control system 150 may beconfigured to reduce the computational burden of the processor 112during noise reduction. Control system 150 may use any approach toreduce computational burden. In some embodiments, where several pixelsof image sensor 104 behave similar manner, the control system 150 mayassociate the same “n” or σ_(actual) values to groups of pixels to easecomputational requirements. These groups of pixels (that are assumed bythe control system 150 to behave similarly) may be preselected or may beselected by a user based on the application. For example, in anapplication of endoscope 100 (or another device that includes imagesensor 104) where computational speed is more important than imagefidelity, a user may prompt the control system 150 to treat pixels thathave incident intensities (or standard deviations at a particularintensity) within a certain range to be similar to ease thecomputational burden.

In some embodiments, the control system 150 may also employ othermethods to ease the computational burden of processor 112. For instance,it is known that binary division is a computationally intensive process.Therefore, an averaging operation (that includes adding “n” number offrames together and dividing the result by “n”) is a computationallyintensive process. However, binary division where the divisor is a powerof two is relatively trivial. This is because, in binary arithmetic,division by two can be performed by a bit shift operation. Therefore, insome embodiments, the control system may round the number of frames “n”to be averaged at any particular intensity up to the closest higherpower of two. The control system 150 may round “n” to the closest higherpower of 2 using any method known in the art. In some embodiments, thecontroller may round “n” to the closest higher power of 2 using equation2 below:

n*=2^({ceil[log) ² (n)]}  (2)

where n* is the number of frames to be averaged at any intensity roundedup to the closest higher power of two (such as, for example 2⁰=1, 2¹=2,2²=4, 2³=8, 2⁴=16, etc.). For example, in embodiments where the numberof frames to be averaged “n” is computed as 7, rounding up the number offrames to be averaged to the closest higher power of two will result in8. And, in embodiments, where the computed value of n is 4, rounding upthe number of frames to be averaged to the closest higher power of two(n*) will result in 4. It should be noted that equation 2 is exemplaryonly, and control system 150 may round the number of frames to beaveraged to the closest higher power of 2 by any means, including usinganother algorithm or equation.

In some embodiments, the control system 150 may compute and store thenumber of frames “n” to be averaged at different intensities to yield atarget standard deviation value of 1 DN (that is, the scatter of thepixel response is less than or equal to one digital number) usingequation 3 below:

n*=ceil(σ_(actual) ²)  (3)

In some embodiments, the control system 150 may compute and store n*,the timber of frames to be averaged at any intensity rounded up to theclosest higher power of two, using equation 4 below:

n*=2{(ceil[log₂(ceil(σ_(actual) ²))]}  (4)

And, based on the observed response of each pixel in an application, thecontrol system 150 may determine the number of frames, n or n*, tominimize noise

FIG. 4 is a graph that illustrates the actual standard deviationσ_(actual) 410 of a pixel 122 as a function of light intensity in anexemplary application. For example, FIG. 4 shows that the observedσ_(actual) 410 of pixel 122 at a light intensity of about 20 cd/ft²about 4 DN, and the σ_(actual) 410 at about 75 cd/ft² is about 14 DN. Itshould be noted that the decrease in observed σ_(actual) values atintensities above about 100 cd/ft² is an artifact of the testing. Thistrend was observed because of signal clipping (that is, in FIG. 4, anintensity of about 100 cd/ft² produced the maximum digital response (2⁸for an 8 bit IC device) and higher values of intensity produced thissame response). FIG. 4 also includes curves 420, 430, 440, 450 thatindicate the number of frames that will have to be averaged at differentintensities, rounded up to the closest higher power of two, (n*) toreduce the noise to within different target standard deviations(σ_(target)). For example, based on FIG. 4, to reduce the noise to aσ_(target) of within 1 DN at a light intensity of 50 cd/ft², 16 frameswill have to be averaged. However, to reduce the noise to a σ_(target)of within 3 DN, only 2 frames will have to be averaged. Curves (or data)similar to that illustrated in FIG. 4 may be used by control system 150to dynamically calculate n* (or “n”) to calibrate an endoscopic imagesensor 104. For example, if a range of intensity values for a particularendoscopic image sensor 104 changes, the relationships in FIG. 4 may beused to select an appropriate value of n* for calibrating the pixels ofthe image sensor in response to the change. The control system 150 mayalso select the number of times to average a response of a pixel at aparticular intensity based on the amount of noise that can be toleratedin an image.

The embodiments described herein are exemplary only, and it will beapparent to those skilled in the art that various modifications andvariations can be made in the disclosed systems and processes withoutdeparting from the scope of the invention. Other embodiments of theinvention will be apparent to those skilled in the art fromconsideration of the specification and practice of the inventiondisclosed herein. It is intended that the specification and examples beconsidered as exemplary only, with a true scope of the invention beingindicated by the following claims.

1-20. (canceled)
 21. A method of calibrating an image sensor including aplurality of pixels, comprising: calibrating a first pixel of the imagesensor, the calibrating the first pixel including: detecting a firstresponse from the first pixel of the image sensor as a result of lighthaving an intensity impinging on the first pixel; receiving an actualstandard deviation of the first response of the first pixel at theintensity of light; determining a first averaging number for the firstpixel at the intensity, the first averaging number being a number ofresponses of the first pixel at the intensity to be averaged to attainan average first response having a first standard deviation less than orequal to a first target value; and determining the average firstresponse of the first pixel using the determined first averaging number;calibrating a second pixel of the image sensor, the calibrating thesecond pixel including: detecting a second response from the secondpixel of the image sensor as a result of light having an intensityimpinging on the second pixel; receiving an actual standard deviation ofthe second response of the second pixel at the intensity of light;determining a second averaging number for the second pixel at theintensity, the second averaging number being a number of responses ofthe second pixel at the intensity to be averaged to attain an averagesecond response having a standard deviation less than or equal to asecond target value; and determining the average second response of thesecond pixel using the determined second averaging number; whereincalibrating the first pixel is done independently of calibrating thesecond pixel.
 22. The method of claim 21, wherein receiving the actualstandard deviation of the first response includes determining the actualstandard deviation of the first response of the first pixel at multipleintensities of incident light and recording the determined actualstandard deviations of the first response.
 23. The method of claim 21,wherein determining the first averaging number includes determining thefirst averaging number using the equation:${n = {{ceil}( \frac{\sigma_{actual}}{\sigma_{target}} )}^{2}},$where n=the first averaging number, σ_(actual)=the actual standarddeviation of the first response at the intensity, σ_(target)=the firsttarget value of standard deviation, and cell is a ceiling function thatrounds a result of (σ_(actual)/σ_(target))² to the next integer greaterthan or equal to the result.
 24. The method of claim 23, whereindetermining the second averaging number includes determining the secondaveraging number using the equation:${n = {{ceil}( \frac{\sigma_{actual}}{\sigma_{target}} )}^{2}},$where n=the second averaging number, σ_(actual)=the actual standarddeviation of the second response at the intensity, σ_(target)=the secondtarget value of standard deviation, and cell is a ceiling function thatrounds a result of (σ_(actual)/σ_(target))² to the next integer greaterthan or equal to the result.
 25. The method of claim 21, whereindetermining the first averaging number includes rounding the determinedfirst averaging number to the closest higher power of two.
 26. Themethod of claim 25, wherein determining the second averaging numberincludes rounding the determined second averaging number to the closesthigher power of two.
 27. The method of claim 21, wherein the firsttarget value is 1 DN.
 28. The method of claim 27, wherein the secondtarget value is 1 DN.
 29. A method of calibrating an image sensor,comprising: detecting a response from a pixel of the image sensor as aresult of light having an intensity impinging on the pixel; receiving anactual standard deviation of the response of the pixel at the intensityof light; determining an averaging number for the pixel at theintensity, the averaging number being a number of responses of the pixelat the intensity to be averaged to attain an average response having astandard deviation less than or equal to a target value; and determiningthe average response of the pixel using the determined averaging number;and wherein determining the actual standard deviation includesindividually determining the actual standard deviation for each pixel ofmultiple pixels of the image sensor at multiple intensities of incidentlight and recording the determined actual standard deviations.
 30. Themethod of claim 29, wherein receiving the actual standard deviationincludes determining the actual standard deviation of the response ofthe pixel at multiple intensities of incident light and recording thedetermined actual standard deviations.
 31. The method of claim 29,wherein determining the averaging number includes individuallydetermining an averaging number for each of the multiple pixels, theaveraging number for each pixel of the multiple pixels being the numberof the responses of the pixel to be averaged to attain an averageresponse for the pixel at the intensity of light incident on the pixel.32. The method of claim 29, wherein determining the averaging numberincludes determining the averaging number using the equation:${n = {{ceil}( \frac{\sigma_{actual}}{\sigma_{target}} )}^{2}},$where n=the averaging number, σ_(actual)=the actual standard deviationat the intensity, σ_(target)=the target value of standard deviation, andcell is a ceiling function that rounds a result of(σ_(actual)/σ_(target))² to the next integer greater than or equal tothe result.
 33. The method of claim 29, wherein determining theaveraging number includes rounding the determined averaging number tothe closest higher power of two.
 34. The method of claim 33, wherein therounding includes rounding the determined averaging number using theequation n*=2^({ceil[log) ² ^((n)]}), where n*=the averaging numberrounded to the closest higher power of two, n=the determined averagingnumber, and cell is a ceiling function that rounds a result of thecalculation to the next integer greater than or equal to the result. 35.The method of claim 29, wherein the target value of standard deviationis the actual standard deviation of a pixel of the image sensor having alowest value of response.
 36. The method of claim 29, wherein the targetvalue is 1 DN.
 37. A method of operating an image sensor, comprising:detecting a response from a pixel of the image sensor as a result oflight having a first intensity impinging on the pixel; obtaining anactual standard deviation of the response of the pixel at the firstintensity, the actual standard deviation being a number indicative of anexpected variation in the response of the pixel; determining a number nat the first intensity, wherein the number n is the number of frames atthe first intensity to be averaged to attain a target standard deviationfor the response at the first intensity; and averaging n number ofresponses from the pixel at the first intensity to obtain an averageresponse from the pixel at the first intensity; and repeating thedetecting, obtaining, determining, and averaging steps for each pixel ofthe image sensor individually of one another.
 38. The method of claim37, wherein obtaining the actual standard deviation includes receivingthe actual standard deviation from a memory operatively coupled to theimage sensor.
 39. The method of claim 37, wherein determining the numbern uses a processor operatively coupled to the image sensor.
 40. Themethod of claim 37, wherein detecting the response includes detectingthe response from the image sensor of an endoscope.